Finite Group Databasebeta

← C101×#19704 #38801855

Subgroups — C101×#19704 #38801855

Order 25856.

704 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3230C211yesmaximal, characteristic, complemented
2C101×#3227C211yesmaximal, characteristic
3C101×#3209C211yesmaximal, characteristic, complemented
4C101×#3206C211yesmaximal, characteristic
5C2×#500×C101C211yesmaximal, characteristic, complemented
6C101×#3131C211yesmaximal, characteristic
7C101×#1723C212yesmaximal, complemented
8C101×#1722C212yesmaximal, complemented
9C101×#1719C212yesmaximal, complemented
10C101×#1718C212yesmaximal, complemented
11C101×#1452C211yesmaximal, characteristic, complemented
12#533×C101C2211yescharacteristic
13#532×C101C2211yescharacteristic
14C2×C4⋊Q8×C101C2211yescharacteristic
15C2×C4⋊Q8×C101C2211yescharacteristic
16#500×C101—22no—
17#500×C101C2212yes—
18#500×C101C2212yes—
19#500×C101C2212yes—
20#498×C101C2212yes—
21#494×C101C2212yes—
22#492×C101C2212yes—
23#488×C101—22no—
24#487×C101C2212yes—
25#487×C101C2212yes—
26#487×C101C2212yes—
27#487×C101C2211yescharacteristic
28#487×C101C2211yescharacteristic
29#486×C101C2212yes—
30#486×C101C2211yescharacteristic
31#486×C101C2211yescharacteristic
32#484×C101—22no—
33#481×C101—22no—
34#477×C101—22no—
35#476×C101—22no—
36#462×C101—22no—
37#461×C101—22no—
38#451×C101—22no—
39#448×C101—22no—
40#431×C101C2211yescharacteristic
41#431×C101C2211yescharacteristic
42C2×#107×C101—22no—
43#416×C101—22no—
44C2×C4×C8×C101C2211yescharacteristic
45#322×C101C2212yes—
46#322×C101C2212yes—
47C2×#41×C101—21no—
48C22×Q8×C101—21no—
49C22×Q8×C101—21no—
50C2×Q16×C101—24no—
51C2×SD16×C101—24no—
52C22×C8×C101D412yes—
53C4⋊Q8×C101—21no—
54C4⋊Q8×C101—21no—
55C4⋊Q8×C101—21no—
56C4⋊Q8×C101—21no—
57C4⋊Q8×C101—21no—
58C4⋊Q8×C101—21no—
59C4⋊Q8×C101C2311yescharacteristic
60C4⋊Q8×C101C2311yescharacteristic
61C4⋊Q8×C101C2312yes—
62C4⋊Q8×C101C2311yescharacteristic
63C4⋊Q8×C101C2312yes—
64#127×C101C2311yescharacteristic
65#125×C101—21no—
66#124×C101—21no—
67C22⋊Q8×C101—21no—
68C22⋊Q8×C101—21no—
69#121×C101—21no—
70#121×C101—21no—
71C4×Q8×C101—21no—
72C4×Q8×C101—21no—
73C4×D4×C101—21no—
74C4×D4×C101—21no—
75#117×C101—21no—
76C2×C4⋊C4×C101—21no—
77C2×C4⋊C4×C101—21no—
78C2×C4⋊C4×C101—21no—
79C2×C4⋊C4×C101—21no—
80C2×C42×C101C2311yescharacteristic
81#107×C101—24no—
82#107×C101—24no—
83#107×C101—24no—
84#106×C101—24no—
85C4⋊C8×C101D412yes—
86C4⋊C8×C101D412yes—
87#103×C101—22no—
88#103×C101—22no—
89#103×C101—24no—
90#103×C101—24no—
91#103×C101—24no—
92#102×C101—22no—
93#102×C101—22no—
94#102×C101—24no—
95C22⋊C8×C101D412yes—
96C22⋊C8×C101D412yes—
97C4×C8×C101D412yes—
98C4×C8×C101C2311yescharacteristic
99C4×C8×C101C2311yescharacteristic
100C4×C8×C101C2312yes—
101C4×C8×C101C2312yes—
102#41×C101—44no—
103C2×Q8×C101—21no—
104C2×Q8×C101—21no—
105C2×Q8×C101—22no—
106C2×Q8×C101—22no—
107C2×Q8×C101—21no—
108C2×Q8×C101—41no—
109C2×Q8×C101—41no—
110C2×Q8×C101—82no—
111C2×Q8×C101—82no—
112C2×D4×C101—21no—
113C2×D4×C101—21no—
114C2×D4×C101—21no—
115C2×D4×C101—41no—
116C22×C4×C101—41no—
117C22×C4×C101—41no—
118C22×C4×C101—41no—
119C22×C4×C101C2×D411yescharacteristic
120C22×C4×C101C2×D411yescharacteristic
121C22×C4×C101C2×D411yescharacteristic
122Q16×C101—84no—
123SD16×C101—84no—
124C2×C8×C101—24no—
125C2×C8×C101C2×D412yes—
126C2×C8×C101C2×D412yes—
127C2×C8×C101C2×D414yes—
128C2×C8×C101C2×D414yes—
129C4⋊C4×C101—21no—
130C4⋊C4×C101—21no—
131C4⋊C4×C101—22no—
132C4⋊C4×C101—21no—
133C4⋊C4×C101—21no—
134C4⋊C4×C101—22no—
135C4⋊C4×C101—21no—
136C4⋊C4×C101—22no—
137C4⋊C4×C101—22no—
138C4⋊C4×C101—21no—
139C4⋊C4×C101—41no—
140C4⋊C4×C101—41no—
141C4⋊C4×C101—41no—
142C4⋊C4×C101—41no—
143C4⋊C4×C101—41no—
144C4⋊C4×C101—41no—
145C22⋊C4×C101—41no—
146C22⋊C4×C101—41no—
147C22⋊C4×C101—41no—
148C42×C101—41no—
149C42×C101C2×D411yescharacteristic
150C42×C101C2×D411yescharacteristic
151C42×C101C2×D411yescharacteristic
152C42×C101C2411yescharacteristic
153C23×C101—41no—
154C23×C101#12711yescharacteristic
155Q8×C101—42no—
156Q8×C101—44no—
157Q8×C101—42no—
158Q8×C101—44no—
159Q8×C101—42no—
160Q8×C101—82no—
161Q8×C101—82no—
162D4×C101—42no—
163D4×C101—42no—
164D4×C101—42no—
165D4×C101—82no—
166C2×C4×C101—22no—
167C2×C4×C101—22no—
168C2×C4×C101—41no—
169C2×C4×C101—41no—
170C2×C4×C101—41no—
171C2×C4×C101—42no—
172C2×C4×C101—42no—
173C2×C4×C101—82no—
174C2×C4×C101—82no—
175C2×C4×C101—82no—
176C2×C4×C101#12711yescharacteristic
177C2×C4×C101#12711yescharacteristic
178C2×C4×C101#12711yescharacteristic
179C2×C4×C101#13714yes—
180C2×C4×C101C22×D411yescharacteristic
181C2×C4×C101C22×D411yescharacteristic
182C2×C4×C101C22×D411yescharacteristic
183C8×C101—22no—
184C8×C101—22no—
185C8×C101—24no—
186C8×C101—24no—
187C22×C101—21no—
188C22×C101—21no—
189C22×C101—81no—
190C22×C101—81no—
191C22×C101—81no—
192C22×C101#49712yes—
193C22×C101C2×#12711yescharacteristic
194C4×C101—21no—
195C4×C101—21no—
196C4×C101—81no—
197C4×C101—82no—
198C4×C101—82no—
199C4×C101—81no—
200C4×C101—81no—
201C4×C101#49712yes—
202C4×C101C2×#13712yes—
203C4×C101#57612yes—
204C4×C101#57812yes—
205#19704C10111yesmaximal, characteristic, direct product factor, Sylow
206C2×C101—22no—
207C2×C101—161no—
208C2×C101C2×#49711yescharacteristic
209C2×C101#315511yescharacteristic
210C2×C101#315611yescharacteristic
211#3230C2×C10111yescharacteristic, complemented
212#3227C2×C10111yescharacteristic
213#3209C2×C10111yescharacteristic, complemented
214#3206C2×C10111yescharacteristic
215C2×#500C2×C10111yescharacteristic, complemented
216#3131C2×C10111yescharacteristic
217#1723C2×C10112yescomplemented
218#1722C2×C10112yescomplemented
219#1719C2×C10112yescomplemented
220#1718C2×C10112yescomplemented
221#1452C2×C10111yescharacteristic, complemented
222C101#1970411yescharacteristic, direct product factor, Sylow
223#533C22×C10111yescharacteristic
224#532C22×C10111yescharacteristic
225C2×C4⋊Q8C22×C10111yescharacteristic
226C2×C4⋊Q8C22×C10111yescharacteristic
227#500—22no—
228#500C22×C10112yes—
229#500C22×C10112yes—
230#500C22×C10112yes—
231#498C22×C10112yes—
232#494C22×C10112yes—
233#492C22×C10112yes—
234#488—22no—
235#487C22×C10111yescharacteristic
236#487C22×C10111yescharacteristic
237#487C22×C10112yes—
238#487C22×C10112yes—
239#487C22×C10112yes—
240#486C22×C10111yescharacteristic
241#486C22×C10111yescharacteristic
242#486C22×C10112yes—
243#484—22no—
244#481—22no—
245#477—22no—
246#476—22no—
247#462—22no—
248#461—22no—
249#451—22no—
250#448—22no—
251#431C22×C10111yescharacteristic
252#431C22×C10111yescharacteristic
253C2×#107—22no—
254#416—22no—
255C2×C4×C8C22×C10111yescharacteristic
256#322C22×C10112yes—
257#322C22×C10112yes—
258C2×#41—21no—
259C22×Q8—21no—
260C22×Q8—21no—
261C2×Q16—24no—
262C2×SD16—24no—
263C22×C8D4×C10112yes—
264C4⋊Q8—21no—
265C4⋊Q8—21no—
266C4⋊Q8—21no—
267C4⋊Q8—21no—
268C4⋊Q8—21no—
269C4⋊Q8—21no—
270C4⋊Q8C23×C10112yes—
271C4⋊Q8C23×C10112yes—
272C4⋊Q8C23×C10111yescharacteristic
273C4⋊Q8C23×C10111yescharacteristic
274C4⋊Q8C23×C10111yescharacteristic
275#127C23×C10111yescharacteristic
276#125—21no—
277#124—21no—
278C22⋊Q8—21no—
279C22⋊Q8—21no—
280#121—21no—
281#121—21no—
282C4×Q8—21no—
283C4×Q8—21no—
284C4×D4—21no—
285C4×D4—21no—
286#117—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C42C23×C10111yescharacteristic
292#107—24no—
293#107—24no—
294#107—24no—
295#106—24no—
296C4⋊C8D4×C10112yes—
297C4⋊C8D4×C10112yes—
298#103—22no—
299#103—22no—
300#103—24no—
301#103—24no—
302#103—24no—
303#102—22no—
304#102—22no—
305#102—24no—
306C22⋊C8D4×C10112yes—
307C22⋊C8D4×C10112yes—
308C4×C8D4×C10112yes—
309C4×C8C23×C10111yescharacteristic
310C4×C8C23×C10111yescharacteristic
311C4×C8C23×C10112yes—
312C4×C8C23×C10112yes—
313#41—44no—
314C2×Q8—21no—
315C2×Q8—21no—
316C2×Q8—22no—
317C2×Q8—22no—
318C2×Q8—21no—
319C2×Q8—41no—
320C2×Q8—41no—
321C2×Q8—82no—
322C2×Q8—82no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4C2×D4×C10111yescharacteristic
331C22×C4C2×D4×C10111yescharacteristic
332C22×C4C2×D4×C10111yescharacteristic
333Q16—84no—
334SD16—84no—
335C2×C8—24no—
336C2×C8C2×D4×C10112yes—
337C2×C8C2×D4×C10112yes—
338C2×C8C2×D4×C10114yes—
339C2×C8C2×D4×C10114yes—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—22no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—22no—
346C4⋊C4—21no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—21no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C4⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C42—41no—
360C42C2×D4×C10111yescharacteristic
361C42C2×D4×C10111yescharacteristic
362C42C2×D4×C10111yescharacteristic
363C42C24×C10111yescharacteristic
364C23—41no—
365C23#127×C10111yescharacteristic
366Q8—42no—
367Q8—44no—
368Q8—42no—
369Q8—44no—
370Q8—42no—
371Q8—82no—
372Q8—82no—
373D4—42no—
374D4—42no—
375D4—42no—
376D4—82no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—82no—
385C2×C4—82no—
386C2×C4—82no—
387C2×C4#127×C10111yescharacteristic
388C2×C4#127×C10111yescharacteristic
389C2×C4#127×C10111yescharacteristic
390C2×C4#137×C10114yes—
391C2×C4C22×D4×C10111yescharacteristic
392C2×C4C22×D4×C10111yescharacteristic
393C2×C4C22×D4×C10111yescharacteristic
394C8—22no—
395C8—22no—
396C8—24no—
397C8—24no—
398C22—21no—
399C22—21no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22#497×C10112yes—
404C22C2×#127×C10111yescharacteristic
405C4—21no—
406C4—21no—
407C4—81no—
408C4—82no—
409C4—82no—
410C4—81no—
411C4—81no—
412C4#497×C10112yes—
413C4C2×#137×C10112yes—
414C4#576×C10112yes—
415C4#578×C10112yes—
416C2—22no—
417C2—161no—
418C2C2×#497×C10111yescharacteristic
419C2C101×#315511yescharacteristic
420C2C101×#315611yescharacteristic
subgroupG/H
center, socleC22×C101C2×#127
commutator, Frattini, cosocleC42C24×C101
prime radical#532×C101C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C2×C42×C101 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C101×#3230C2semidirect
3. C101×#3209C2semidirect
5. C2×#500×C101C2semidirect
7. C101×#1723C2semidirect
8. C101×#1722C2semidirect
9. C101×#1719C2semidirect
10. C101×#1718C2semidirect
11. C101×#1452C2semidirect
205. #19704C101direct (N × H)
211. #3230C2×C101semidirect
213. #3209C2×C101semidirect
215. C2×#500C2×C101semidirect
217. #1723C2×C101semidirect
218. #1722C2×C101semidirect
219. #1719C2×C101semidirect
220. #1718C2×C101semidirect
221. #1452C2×C101semidirect
222. C101#19704direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C101×#32302
C101×#32272
C101×#32092
C101×#32062
C2×#500×C1012
C101×#31312
C101×#17232
C101×#17222
C101×#17192
C101×#17182
C101×#14522
#19704101